////////////////////////////////////////////////////////////////////////
//
// Copyright (C) 2016-2024 The Octave Project Developers
//
// See the file COPYRIGHT.md in the top-level directory of this
// distribution or <https://octave.org/copyright/>.
//
// This file is part of Octave.
//
// Octave is free software: you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// Octave is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with Octave; see the file COPYING.  If not, see
// <https://www.gnu.org/licenses/>.
//
////////////////////////////////////////////////////////////////////////

#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif

#include "oct-string.h"

#include <algorithm>
#include <cctype>
#include <cstring>
#include <iomanip>
#include <string>
#include <unordered_set>

#include "Array.h"
#include "iconv-wrappers.h"
#include "lo-ieee.h"
#include "lo-mappers.h"
#include "oct-locbuf.h"
#include "uniconv-wrappers.h"
#include "unistr-wrappers.h"
#include "unwind-prot.h"

template <typename T>
static bool
str_data_cmp (const typename T::value_type *a, const typename T::value_type *b,
              const typename T::size_type n)
{
  for (typename T::size_type i = 0; i < n; ++i)
    if (a[i] != b[i])
      return false;
  return true;
}

template <typename T>
static bool
str_data_cmpi (const typename T::value_type *a, const typename T::value_type *b,
               const typename T::size_type n)
{
  for (typename T::size_type i = 0; i < n; ++i)
    if (std::tolower (a[i]) != std::tolower (b[i]))
      return false;
  return true;
}


// Templates to handle std::basic_string, std::vector, Array, and char*.
template <typename T>
typename T::size_type
numel (const T& str)
{
  return str.size ();
}

template <>
octave_idx_type
numel (const Array<char>& str)
{
  return str.numel ();
}

template <typename T>
typename T::size_type
strlen (const typename T::value_type *str)
{
  return std::strlen (str);
}

template <typename T>
bool
sizes_cmp (const T& str_a, const T& str_b)
{
  return str_a.size () == str_b.size ();
}

template <>
bool
sizes_cmp (const Array<char>& str_a, const Array<char>& str_b)
{
  return str_a.dims () == str_b.dims ();
}

template <typename T>
bool
sizes_cmp (const T& str_a, const typename T::value_type *str_b)
{
  return str_a.size () == strlen<T> (str_b);
}

template <>
bool
sizes_cmp (const Array<char>& str_a, const char *str_b)
{
  return (str_a.isvector () && str_a.rows () == 1
          && str_a.numel () == strlen<Array<char>> (str_b));
}


template<typename T>
bool
octave::string::strcmp (const T& str_a, const T& str_b)
{
  return (sizes_cmp (str_a, str_b)
          && str_data_cmp<T> (str_a.data (), str_b.data (), numel (str_a)));
}

template<typename T>
bool
octave::string::strcmp (const T& str_a, const typename T::value_type *str_b)
{
  return (sizes_cmp (str_a, str_b)
          && str_data_cmp<T> (str_a.data (), str_b, numel (str_a)));
}


template<typename T>
bool
octave::string::strcmpi (const T& str_a, const T& str_b)
{
  return (sizes_cmp (str_a, str_b)
          && str_data_cmpi<T> (str_a.data (), str_b.data (), numel (str_a)));
}

template<typename T>
bool
octave::string::strcmpi (const T& str_a, const typename T::value_type *str_b)
{
  return (sizes_cmp (str_a, str_b)
          && str_data_cmpi<T> (str_a.data (), str_b, numel (str_a)));
}


template<typename T>
bool
octave::string::strncmp (const T& str_a, const T& str_b,
                         const typename T::size_type n)
{
  typename T::size_type neff;
  auto len_a = numel (str_a);
  auto len_b = numel (str_b);
  neff = std::min (std::max (len_a, len_b), n);

  return (len_a >= neff && len_b >= neff
          && str_data_cmp<T> (str_a.data (), str_b.data (), neff));
}

template<typename T>
bool
octave::string::strncmp (const T& str_a, const typename T::value_type *str_b,
                         const typename T::size_type n)
{
  typename T::size_type neff;
  auto len_a = numel (str_a);
  auto len_b = strlen<T> (str_b);
  neff = std::min (std::max (len_a, len_b), n);

  return (len_a >= neff && len_b >= neff
          && str_data_cmp<T> (str_a.data (), str_b, neff));
}


template<typename T>
bool
octave::string::strncmpi (const T& str_a, const T& str_b,
                          const typename T::size_type n)
{
  typename T::size_type neff;
  auto len_a = numel (str_a);
  auto len_b = numel (str_b);
  neff = std::min (std::max (len_a, len_b), n);

  return (len_a >= neff && len_b >= neff
          && str_data_cmpi<T> (str_a.data (), str_b.data (), neff));
}

template<typename T>
bool
octave::string::strncmpi (const T& str_a, const typename T::value_type *str_b,
                          const typename T::size_type n)
{
  typename T::size_type neff;
  auto len_a = numel (str_a);
  auto len_b = strlen<T> (str_b);
  neff = std::min (std::max (len_a, len_b), n);

  return (len_a >= neff && len_b >= neff
          && str_data_cmpi<T> (str_a.data (), str_b, neff));
}


// Instantiations we need
#define INSTANTIATE_OCTAVE_STRING(T, API)                                     \
  template API bool octave::string::strcmp<T> (const T&, const T&);           \
  template API bool                                                           \
  octave::string::strcmp<T> (const T&, const typename T::value_type*);        \
  template API bool octave::string::strcmpi<T> (const T&, const T&);          \
  template API bool                                                           \
  octave::string::strcmpi<T> (const T&, const typename T::value_type*);       \
  template API bool                                                           \
  octave::string::strncmp<T> (const T&, const T&,                             \
                              const typename T::size_type);                   \
  template API bool                                                           \
  octave::string::strncmp<T> (const T&, const typename T::value_type*,        \
                              const typename T::size_type);                   \
  template API bool                                                           \
  octave::string::strncmpi<T> (const T&, const T&,                            \
                               const typename T::size_type n);                \
  template API bool                                                           \
  octave::string::strncmpi<T> (const T&, const typename T::value_type*,       \
                               const typename T::size_type);

// We could also instantiate std::vector<char> but would it be
// useful for anyone?
INSTANTIATE_OCTAVE_STRING(std::string, OCTAVE_API)
INSTANTIATE_OCTAVE_STRING(Array<char>, OCTAVE_API)

#undef INSTANTIATE_OCTAVE_STRING

static inline bool
is_imag_unit (int c)
{ return c == 'i' || c == 'j'; }

static double
single_num (std::istringstream& is)
{
  double num = 0.0;

  char c = is.peek ();

  // Skip spaces.
  while (isspace (c))
    {
      is.get ();
      c = is.peek ();
    }

  if (std::toupper (c) == 'I')
    {
      // It's infinity.
      is.get ();
      char c1 = is.get ();
      char c2 = is.get ();
      if (std::tolower (c1) == 'n' && std::tolower (c2) == 'f')
        {
          num = octave::numeric_limits<double>::Inf ();
          is.peek (); // May set EOF bit.
        }
      else
        is.setstate (std::ios::failbit); // indicate that read has failed.
    }
  else if (c == 'N')
    {
      // It's NA or NaN
      is.get ();
      char c1 = is.get ();
      if (c1 == 'A')
        {
          num = octave_NA;
          is.peek (); // May set EOF bit.
        }
      else
        {
          char c2 = is.get ();
          if (c1 == 'a' && c2 == 'N')
            {
              num = octave::numeric_limits<double>::NaN ();
              is.peek (); // May set EOF bit.
            }
          else
            is.setstate (std::ios::failbit); // indicate that read has failed.
        }
    }
  else
    is >> num;

  return num;
}

static std::istringstream&
extract_num (std::istringstream& is, double& num, bool& imag, bool& have_sign)
{
  have_sign = imag = false;

  char c = is.peek ();

  // Skip leading spaces.
  while (isspace (c))
    {
      is.get ();
      c = is.peek ();
    }

  bool negative = false;

  // Accept leading sign.
  if (c == '+' || c == '-')
    {
      have_sign = true;
      negative = c == '-';
      is.get ();
      c = is.peek ();
    }

  // Skip spaces after sign.
  while (isspace (c))
    {
      is.get ();
      c = is.peek ();
    }

  // Imaginary number (i*num or just i), or maybe 'inf'.
  if (c == 'i')
    {
      // possible infinity.
      is.get ();
      c = is.peek ();

      if (is.eof ())
        {
          // just 'i' and string is finished.  Return immediately.
          imag = true;
          num = (negative ? -1.0 : 1.0);
          return is;
        }
      else
        {
          if (std::tolower (c) != 'n')
            imag = true;
          is.unget ();
        }
    }
  else if (c == 'j')
    imag = true;

  // It's i*num or just i
  if (imag)
    {
      is.get ();
      c = is.peek ();
      // Skip spaces after imaginary unit.
      while (isspace (c))
        {
          is.get ();
          c = is.peek ();
        }

      if (c == '*')
        {
          // Multiplier follows, we extract it as a number.
          is.get ();
          num = single_num (is);
          if (is.good ())
            c = is.peek ();
        }
      else
        num = 1.0;
    }
  else
    {
      // It's num, num*i, or numi.
      num = single_num (is);
      if (is.good ())
        {
          c = is.peek ();

          // Skip spaces after number.
          while (isspace (c))
            {
              is.get ();
              c = is.peek ();
            }

          if (c == '*')
            {
              is.get ();
              c = is.peek ();

              // Skip spaces after operator.
              while (isspace (c))
                {
                  is.get ();
                  c = is.peek ();
                }

              if (is_imag_unit (c))
                {
                  imag = true;
                  is.get ();
                  c = is.peek ();
                }
              else
                is.setstate (std::ios::failbit); // indicate read has failed.
            }
          else if (is_imag_unit (c))
            {
              imag = true;
              is.get ();
              c = is.peek ();
            }
        }
    }

  if (is.good ())
    {
      // Skip trailing spaces.
      while (isspace (c))
        {
          is.get ();
          c = is.peek ();
        }
    }

  if (negative)
    num = -num;

  return is;
}

static inline void
set_component (Complex& c, double num, bool imag)
{
#if defined (HAVE_CXX_COMPLEX_SETTERS)
  if (imag)
    c.imag (num);
  else
    c.real (num);
#elif defined (HAVE_CXX_COMPLEX_REFERENCE_ACCESSORS)
  if (imag)
    c.imag () = num;
  else
    c.real () = num;
#else
  if (imag)
    c = Complex (c.real (), num);
  else
    c = Complex (num, c.imag ());
#endif
}

Complex
octave::string::str2double (const std::string& str_arg)
{
  Complex val (0.0, 0.0);

  std::string str = str_arg;

  // FIXME: removing all commas doesn't allow actual parsing.
  //        Example: "1,23.45" is wrong, but passes Octave.
  str.erase (std::remove (str.begin (), str.end(), ','), str.end ());
  std::istringstream is (str);

  double num;
  bool i1, i2, s1, s2;

  if (is.eof ())
    val = octave::numeric_limits<double>::NaN ();
  else if (! extract_num (is, num, i1, s1))
    val = octave::numeric_limits<double>::NaN ();
  else
    {
      set_component (val, num, i1);

      if (! is.eof ())
        {
          if (! extract_num (is, num, i2, s2) || i1 == i2 || ! s2)
            val = octave::numeric_limits<double>::NaN ();
          else
            set_component (val, num, i2);
        }
    }

  return val;
}

std::string
octave::string::u8_to_encoding (const std::string& who,
                                const std::string& u8_string,
                                const std::string& encoding)
{
  const uint8_t *src = reinterpret_cast<const uint8_t *>
                       (u8_string.c_str ());
  std::size_t srclen = u8_string.length ();

  std::size_t length;
  char *native_str = octave_u8_conv_to_encoding (encoding.c_str (), src,
                                                 srclen, &length);

  if (! native_str)
    {
      if (errno == ENOSYS)
        (*current_liboctave_error_handler)
          ("%s: iconv() is not supported. Installing GNU libiconv and then "
           "re-compiling Octave could fix this.", who.c_str ());
      else
        (*current_liboctave_error_handler)
          ("%s: converting from UTF-8 to codepage '%s' failed: %s",
           who.c_str (), encoding.c_str (), std::strerror (errno));
    }

  octave::unwind_action free_native_str ([=] () { ::free (native_str); });

  std::string retval = std::string (native_str, length);

  return retval;
}

std::string
octave::string::u8_from_encoding (const std::string& who,
                                  const std::string& native_string,
                                  const std::string& encoding)
{
  const char *src = native_string.c_str ();
  std::size_t srclen = native_string.length ();

  std::size_t length;
  uint8_t *utf8_str = octave_u8_conv_from_encoding (encoding.c_str (), src,
                                                    srclen, &length);
  if (! utf8_str)
    {
      if (errno == ENOSYS)
        (*current_liboctave_error_handler)
          ("%s: iconv() is not supported. Installing GNU libiconv and then "
           "re-compiling Octave could fix this.", who.c_str ());
      else
        (*current_liboctave_error_handler)
          ("%s: converting from codepage '%s' to UTF-8 failed: %s",
           who.c_str (), encoding.c_str (), std::strerror (errno));
    }

  octave::unwind_action free_utf8_str ([=] () { ::free (utf8_str); });

  std::string retval = std::string (reinterpret_cast<char *> (utf8_str), length);

  return retval;
}

unsigned int
octave::string::u8_validate (const std::string& who,
                             std::string& in_str,
                             const octave::string::u8_fallback_type type)
{
  std::string out_str;

  unsigned int num_replacements = 0;
  const char *in_chr = in_str.c_str ();
  const char *inv_utf8 = in_chr;
  const char *const in_end = in_chr + in_str.length ();
  while (inv_utf8 && in_chr < in_end)
    {
      inv_utf8 = reinterpret_cast<const char *>
          (octave_u8_check_wrapper (reinterpret_cast<const uint8_t *> (in_chr),
                                    in_end - in_chr));

      if (inv_utf8 == nullptr)
        out_str.append (in_chr, in_end - in_chr);
      else
        {
          num_replacements++;
          out_str.append (in_chr, inv_utf8 - in_chr);
          in_chr = inv_utf8 + 1;

          if (type == U8_REPLACEMENT_CHAR)
            out_str.append ("\xef\xbf\xbd");
          else if (type == U8_ISO_8859_1)
            {
              std::string fallback = "iso-8859-1";
              std::size_t lengthp;
              uint8_t *val_utf8 = octave_u8_conv_from_encoding
                                    (fallback.c_str (), inv_utf8, 1, &lengthp);

              if (! val_utf8)
                (*current_liboctave_error_handler)
                  ("%s: converting from codepage '%s' to UTF-8 failed: %s",
                   who.c_str (), fallback.c_str (), std::strerror (errno));

              octave::unwind_action free_val_utf8
                ([=] () { ::free (val_utf8); });

              out_str.append (reinterpret_cast<const char *> (val_utf8),
                              lengthp);
            }
        }
    }

  in_str = out_str;
  return num_replacements;
}

std::string
octave::string::u16_to_encoding (const std::string& who,
                                 const std::u16string& u16_string,
                                 const std::string& encoding)
{
  const uint16_t *src = reinterpret_cast<const uint16_t *>
                        (u16_string.c_str ());
  std::size_t srclen = u16_string.length ();

  std::size_t length;
  char *native_str = octave_u16_conv_to_encoding (encoding.c_str (), src,
                                                  srclen, &length);

  if (! native_str)
    {
      if (errno == ENOSYS)
        (*current_liboctave_error_handler)
          ("%s: iconv() is not supported. Installing GNU libiconv and then "
           "re-compiling Octave could fix this.", who.c_str ());
      else
        (*current_liboctave_error_handler)
          ("%s: converting from UTF-16 to codepage '%s' failed: %s",
           who.c_str (), encoding.c_str (), std::strerror (errno));
    }

  octave::unwind_action free_native_str ([=] () { ::free (native_str); });

  std::string retval = std::string (native_str, length);

  return retval;
}

std::vector<std::string>
octave::string::get_encoding_list ()
{
  static std::vector<std::string> encoding_list;

  if (encoding_list.empty ())
    {
#if defined (HAVE_ICONVLIST)
      // get number of supported encodings
      std::size_t count = 0;
      octave_iconvlist_wrapper (
        [] (unsigned int num, const char * const *, void *data) -> int
          {
            std::size_t *count_ptr = static_cast<std::size_t *> (data);
            *count_ptr = num;
            return 0;
          },
        &count);

      if (count == static_cast<size_t> (-1))
        {
          encoding_list.push_back ("UTF-8");
          return encoding_list;
        }

#  if defined (HAVE_ICONV_CANONICALIZE)
      // use unordered_set to skip canonicalized aliases
      std::unordered_set<std::string> encoding_set;
      encoding_set.reserve (count);

      // populate vector with name of encodings
      octave_iconvlist_wrapper (
        [] (unsigned int num, const char * const *names, void *data) -> int
          {
            std::unordered_set<std::string> *encoding_set_ptr
              = static_cast<std::unordered_set<std::string> *> (data);
            for (std::size_t i = 0; i < num; i++)
              {
                const char *canonicalized_enc
                  = octave_iconv_canonicalize_wrapper (names[i]);
                encoding_set_ptr->insert (canonicalized_enc);
              }
            return 0;
          },
        &encoding_set);

      encoding_list.assign (encoding_set.begin (), encoding_set.end ());
#  endif

#else
      // Use hardcoded list of encodings as a fallback for platforms without
      // iconvlist (or another way of programmatically querrying a list of
      // supported encodings).
      // This list is inspired by the encodings supported by Geany.
      encoding_list
        = {"ISO-8859-1",
           "ISO-8859-2",
           "ISO-8859-3",
           "ISO-8859-4",
           "ISO-8859-5",
           "ISO-8859-6",
           "ISO-8859-7",
           "ISO-8859-8",
           "ISO-8859-9",
           "ISO-8859-10",
           "ISO-8859-13",
           "ISO-8859-14",
           "ISO-8859-15",
           "ISO-8859-16",

           "UTF-7",
           "UTF-8",
           "UTF-16LE",
           "UTF-16BE",
           "UTF-32LE",
           "UTF-32BE",
           "UCS-2LE",
           "UCS-2BE",

           "ARMSCII-8",
           "BIG5",
           "BIG5-HKSCS",
           "CP866",

           "EUC-JP",
           "EUC-KR",
           "EUC-TW",

           "GB18030",
           "GB_2312-80",
           "GBK",
           "HZ",

           "IBM850",
           "IBM852",
           "IBM855",
           "IBM857",
           "IBM862",
           "IBM864",

           "ISO-2022-JP",
           "ISO-2022-KR",
           "JOHAB",
           "KOI8-R",
           "KOI8-U",

           "SHIFT_JIS",
           "TCVN",
           "TIS-620",
           "UHC",
           "VISCII",

           "CP1250",
           "CP1251",
           "CP1252",
           "CP1253",
           "CP1254",
           "CP1255",
           "CP1256",
           "CP1257",
           "CP1258",

           "CP932"
           };

      // FIXME: Should we check whether those are actually valid encoding
      // identifiers?
#endif

      // sort list of encodings
      std::sort (encoding_list.begin (), encoding_list.end ());
    }

  return encoding_list;
}

typedef octave::string::codecvt_u8::InternT InternT;
typedef octave::string::codecvt_u8::ExternT ExternT;
typedef octave::string::codecvt_u8::StateT StateT;

typename std::codecvt<InternT, ExternT, StateT>::result
octave::string::codecvt_u8::do_out
  (StateT& /* state */,
   const InternT* from, const InternT* from_end, const InternT*& from_next,
   ExternT* to, ExternT* to_end, ExternT*& to_next) const
{
  to_next = to;
  if (from_end <= from)
    {
      from_next = from_end;
      return std::codecvt<InternT, ExternT, StateT>::noconv;
    }

  // Check if buffer ends in a complete UTF-8 surrogate.
  // FIXME: If this is the last call before a stream is closed, we should
  //        convert trailing bytes even if they look incomplete.
  //        How can we detect that?
  std::size_t pop_end = 0;
  if ((*(from_end-1) & 0b10000000) == 0b10000000)
    {
      // The last byte is part of a surrogate. Check if it is complete.

      // number of bytes of the surrogate in the buffer
      std::size_t num_bytes_in_buf = 1;
      // Find initial byte of surrogate
      while (((*(from_end-num_bytes_in_buf) & 0b11000000) != 0b11000000)
             && (num_bytes_in_buf < 4)
             && (from_end-num_bytes_in_buf > from))
        num_bytes_in_buf++;

      // If the start of the surrogate is not in the buffer, we need to
      // continue with the invalid UTF-8 sequence to avoid an infinite loop.
      // Check if we found an initial byte and if there are enough bytes in the
      // buffer to complete the surrogate.
      if ((((*(from_end-num_bytes_in_buf) & 0b11100000) == 0b11000000)
           && (num_bytes_in_buf < 2))  // incomplete 2-byte surrogate
          || (((*(from_end-num_bytes_in_buf) & 0b11110000) == 0b11100000)
              && (num_bytes_in_buf < 3))  // incomplete 3-byte surrogate
          || (((*(from_end-num_bytes_in_buf) & 0b11111000) == 0b11110000)
              && (num_bytes_in_buf < 4)))  // incomplete 4-byte surrogate
        pop_end = num_bytes_in_buf;
    }
  from_next = from_end - pop_end;

  std::size_t srclen = (from_end-from-pop_end) * sizeof (InternT);
  std::size_t length = (to_end-to) * sizeof (ExternT);
  if (srclen < 1 || length < 1)
    return std::codecvt<InternT, ExternT, StateT>::partial;

  // Convert from UTF-8 to output encoding
  const uint8_t *u8_str = reinterpret_cast<const uint8_t *> (from);
  char *enc_str = octave_u8_conv_to_encoding (m_enc.c_str (), u8_str, srclen,
                                              &length);

  if (length < 1)
    return std::codecvt<InternT, ExternT, StateT>::partial;

  size_t max = (to_end - to) * sizeof (ExternT);
  // FIXME: If the output encoding is a multibyte or variable byte encoding,
  //        we should ensure that we don't cut off a "partial" surrogate from
  //        the output.
  //        Can this ever happen?
  if (length < max)
    max = length;

  // copy conversion result to output
  std::copy_n (enc_str, max, to);
  ::free (enc_str);

  from_next = from + srclen;
  to_next = to + max;

  return ((pop_end > 0 || max < length)
          ? std::codecvt<InternT, ExternT, StateT>::partial
          : std::codecvt<InternT, ExternT, StateT>::ok);
}

typename std::codecvt<InternT, ExternT, StateT>::result
octave::string::codecvt_u8::do_in
  (StateT& /* state */,
   const ExternT* from, const ExternT* from_end, const ExternT*& from_next,
   InternT* to, InternT* to_end, InternT*& to_next) const
{
  // Convert from input encoding to UTF-8
  std::size_t srclen = (from_end-from) * sizeof (ExternT);
  std::size_t lengthp = (to_end-to) * sizeof (InternT);
  const char *enc_str = reinterpret_cast<const char *> (from);
  uint8_t *u8_str = octave_u8_conv_from_encoding (m_enc.c_str (),
                                                  enc_str, srclen, &lengthp);

  std::size_t max = to_end - to;
  if (lengthp < max)
    max = lengthp;

  // copy conversion result to output
  std::copy_n (u8_str, max, to);
  ::free (u8_str);

  from_next = from + srclen;
  to_next = to + max;

  return std::codecvt<InternT, ExternT, StateT>::ok;
}

int octave::string::codecvt_u8::do_length
  (StateT& /* state */, const ExternT *src, const ExternT *end,
   std::size_t max) const
{
  // return number of external characters that produce MAX internal ones
  std::size_t srclen = end-src;
  OCTAVE_LOCAL_BUFFER (std::size_t, offsets, srclen);
  std::size_t lengthp = max;
  octave_u8_conv_from_encoding_offsets (m_enc.c_str (), src, srclen, offsets,
                                        &lengthp);
  std::size_t ext_char;
  for (ext_char = 0; ext_char < srclen; ext_char++)
    {
      if (offsets[ext_char] != static_cast<size_t> (-1)
          && offsets[ext_char] >= max)
        break;
    }

  return ext_char;
}


template <typename T>
std::string
rational_approx (T val, int len)
{
  std::string s;

  if (len <= 0)
    len = 10;

  static const T out_of_range_top
    = static_cast<T> (std::numeric_limits<int>::max ()) + 1.;
  static const T out_of_range_bottom
    = static_cast<T> (std::numeric_limits<int>::min ()) - 1.;
  if (octave::math::isinf (val))
    {
      if (val > 0)
        s = "1/0";
      else
        s = "-1/0";
    }
  else if (octave::math::isnan (val))
    s = "0/0";
  else if (val <= out_of_range_bottom || val >= out_of_range_top
           || octave::math::x_nint (val) == val)
    {
      std::ostringstream buf;
      buf.flags (std::ios::fixed);
      buf << std::setprecision (0) << octave::math::round (val);
      s = buf.str ();
    }
  else
    {
      T lastn = 1;
      T lastd = 0;
      T n = octave::math::round (val);
      T d = 1;
      T frac = val - n;

      std::ostringstream init_buf;
      init_buf.flags (std::ios::fixed);
      init_buf << std::setprecision (0) << static_cast<int> (n);
      s = init_buf.str ();

      while (true)
        {
          T flip = 1 / frac;
          T step = octave::math::round (flip);
          T nextn = n;
          T nextd = d;

          // Have we converged to 1/intmax ?
          if (std::abs (flip) > out_of_range_top)
            {
              lastn = n;
              lastd = d;
              break;
            }

          frac = flip - step;
          n = step * n + lastn;
          d = step * d + lastd;
          lastn = nextn;
          lastd = nextd;

          std::ostringstream buf;
          buf.flags (std::ios::fixed);
          buf << std::setprecision (0) << static_cast<int> (n)
              << '/' << static_cast<int> (d);

          if (n < 0 && d < 0)
            {
              // Double negative, string can be two characters longer.
              if (buf.str ().length () > static_cast<unsigned int> (len + 2))
                break;
            }
          else
            {
              if (buf.str ().length () > static_cast<unsigned int> (len))
                break;
            }

          if (std::abs (n) >= out_of_range_top
              || std::abs (d) >= out_of_range_top)
            break;

          s = buf.str ();
        }

      if (lastd < 0)
        {
          // Move negative sign from denominator to numerator
          lastd = - lastd;
          lastn = - lastn;
          std::ostringstream buf;
          buf.flags (std::ios::fixed);
          buf << std::setprecision (0) << static_cast<int> (lastn)
              << '/' << static_cast<int> (lastd);
          s = buf.str ();
        }
    }

  return s;
}

// instantiate the template for float and double
template OCTAVE_API std::string rational_approx <float> (float val, int len);
template OCTAVE_API std::string rational_approx <double> (double val, int len);
